背包类问题的并行O(25n/6)时间-空间-处理机折衷

摘要

将串行动态二表算法应用于并行三表算法的设计中,提出一种求解背包、精确的可满足性和集覆盖等背包类NP完全问题的并行三表六子表算法.基于EREW-PRAM模型,该算法可使用O(2n/8)的处理机在O(27n/16)的时间和O(213n/48)的空间求解n维背包类问题,其时间-空间-处理机折衷为O(25n/6).与现有文献的性能对比分析表明,该算法极大地提高了并行求解背包类问题的时间-空间-处理机折衷性能.由于该算法能够破解更高维数的背包类公钥和数字水印系统,其结论在密钥分析领域具有一定的理论和实际意义.%A general-purpose parallel three-list six-table algorithm that can solve a number of knapsack-like NP-complete problems is developed in this paper. This kind of problems includes knapsack problem, exact satisfiability problem, set covering problem, etc. Running on an EREW PRAM model, The proposed parallel algorithm can find a solution of these problems of size n in O(27n/16) time, with O(213n/48) space and O(2n/8) processors, resulting in a time-space-processor tradeoff of O(25n/6). The performance analysis and comparisons show that it is both work and space efficient, and thus is an improved result over the past researches. Since it can break greater variables knapsack-based cryptosystems and watermark, the new algorithm has some cryptanalytic significance.